1. Field of the Invention
The present invention relates to an apparatus for generating an arbitrary parameter curve represented by a Bezier curve used to generate an outline font character for use in OA (Office Automation) equipment such as the printer of a wordprocessor or for use in the field of design using a CAD.
2. Description of the Related Art
A parameter curve represented by a polynomial can be generally represented by a Bezier curve. A Bezier curve P(t) of an nth order (n is a positive integer) as shown in FIG. 15, is a curve represented by an nth-order function of a parameter t (0.ltoreq.t.ltoreq. 1) and is defined by the following equation using coordinates of (n+1) control points P0, P1, . . . , Pn in an m-dimensional space: ##EQU1##
This curve was initially used in only the field of design using a CAD. In recent years, however, the curve is used in, e.g., an outline font of a high-quality character obtained by smoothing an outline of a printed character in the field of OA equipment, and a strong demand has arisen for generating a curve on the bit map at high speed.
Since the Bezier curve is conventionally generated by software processing using a computer, the processing speed is low.
In order to perform hardware processing without using a computer, equation (1) may be calculated by using a multiplier. In this case, however, the amount of hardware required is undesirably increased since a multiplier is required. In addition, multiplication must be performed (n .times. m) times for each control point, and addition is also required, resulting in a low processing speed. Furthermore, in the method of performing hardware processing by using a multiplier, it is difficult to determine an adequate unit value of the parameter t so that continuous points are generated to form a curve on the bit map without overlapping each other.
Alternatively, processing may be performed such that coordinate points are calculated by using a multiplier for only several values of the parameter t and points between the coordinate points are obtained by linear interpolation. In this case, however, a DDA (digital differential analyzer) is required in addition to a multiplier, resulting in a large amount of hardware. In addition, it is difficult to determine the value of t so that continuous short straight lines form a polyline sufficiently close to a curve.
As described above, in the case of generating a parameter curve by software processing using a computer, the processing speed is low. In the case of performing calculations by using exclusive hardware to generate a parameter curve, the amount of is increased, the processing speed is reduced, and it becomes difficult to determine an adequate unit value of the parameter t.